Third‐order sensitivity analysis for robust aerodynamic design using continuous adjoint

Robust design problems in aerodynamics are associated with the design variables, which control the shape of an aerodynamic body, and also with the so‐called environmental variables, which account for uncertainties. In this kind of problems, the set of design variables, which leads to optimal performance, taking into account possible variations in the environmental variables, is sought. One of the possible ways to solve this problem is by means of the second‐order second‐moment approach, which requires first‐order and second‐order derivatives of the objective function with respect to the environmental variables. Should the minimization problem be solved using a gradient‐based method, algorithms for the computation of up to third‐order sensitivity derivatives (twice with respect to the environmental variables and once with respect to the shape controlling design variables) must be devised. In this paper, a combination of the continuous adjoint variable method and direct differentiation to compute the third‐order sensitivities is proposed. This is shown to be the most efficient among all alternative methods provided that the environmental variables are much less than the design ones. Apart from presenting the method formulation, this paper focuses on the assessment of the so‐computed up‐to third‐order mixed derivatives through comparison with costly finite‐difference schemes. To this end, the robust design of a two‐dimensional duct is performed. Then, using the validated method, the robust design of a two‐dimensional cascade airfoil is demonstrated. Although both cases are handled as inverse design problems, the method can be extended to other objective functions or three‐dimensional problems in a straightforward manner. Copyright © 2012 John Wiley & Sons, Ltd.     

On safe tractable approximations of chance constraints

A natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem, where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 − ?. While being attractive from modeling viewpoint, chance constrained problems “as they are” are, in general, computationally intractable. In this survey paper, we overview several simulation-based and simulation-free computationally tractable approximations of chance constrained convex programs, primarily, those of chance constrained linear, conic quadratic and semidefinite programming.     

A 3D Luminescent Metal‐organic Framework Constructed from Cu4I4 Cubane Clusters and Triangular Imidazole Ligand

Abstract . The solvothermal reaction between cuprous iodide and the rigid triangular imidazole ligand in mixed N,N′‐dimethylacetamide (DMA)‐acetonitrile solvent leads to the isolation of the 3D metal‐organic framework [(Cu₄I₄)₃(TIPA)₄] · 7DMA ( 1 ) [TIPA = tri(4‐imidazolylphenyl) amine], which was characterized by elemental analysis, IR spectroscopy, powder X‐ray diffraction, and single‐crystal X‐ray diffraction. Topologically, the structure of 1 is an unprecedented 3,3,4,4‐connected net with a point symbol of {4.8.10}₂{4.8²}₂{4².8².10²}₂{8⁴.12²}. Compound 1 exhibits orange‐red photoluminescence with an emission maximum at 622 nm at room temperature.     

Preparation of BiVO4/MIL‐125(Ti) composite with enhanced visible‐light photocatalytic activity for dye degradation

Because of their desired features, including very specific surface areas and designable framework architecture together with their possibility to be functionalized, Metal Framework (MOF) is a promising platform for supporting varied materials in respect of catalytic applications in water treatment. In this work, a novel visible‐light‐responsive photocatalyst that comprised BiVO₄ together with MIL‐125(Ti), was synthesized by a two‐step hydrothermal approach. The characterization of as‐obtained samples as performed by X‐ray diffraction, scanning electron microscopy, high resolution transmission electron microscopy, Fourier transform infrared spectroscope, X‐ray photoelectron spectroscopy and ultraviolet‐visible diffuse reflection spectra. Rhodamine B was selected being a target for the evaluation of the photocatalytic function of as‐developed photocatalyst. The photocatalytic reaction parameters, for example, the content of BiVO₄ as well as initial concentration of Rhodamine B was researched. The composite photocatalyst possessing Bi:Ti molar ratio of 3:2 brought to light the fact that the greatest photocatalytic activity had the ability to degrade 92% of Rhodamine B in 180 min. In addition to that, the BiVO₄/MIL‐125(Ti) composite could keep its photocatalytic activity during the recycling test. The phenomenon of disintegration of the photo‐generated charges in the BiVO₄/MIL‐125(Ti) composite was brought to discussion as well.     

Efficient removal of crystal violet and methylene blue from wastewater by ultrasound nanoparticles Cu-MOF in comparison with mechanosynthesis method

The present investigation reports the synthesis of CuBTC (BTC = 1,3,5-benzenetricarboxylate) metal–organic frameworks (MOFs) under solid-state conditions and ultrasound irradiation. Herein, we study uptake and release properties of crystal violet (CV) and methylene blue (MB) from ultrasound nano-CuBTC MOF in comparison with mechanosynthesis method (bulk structure). The ultrasound-assisted methods give a decrease in the surface area as calculated from the reduced nitrogen adsorption capability. In comparison, the uptake of guest molecules on ultrasound nano-CuBTC is remarkable and clearly exceeds that of bulk structure in the aqueous solution of guests. In bulk compound the channel length is increased so that the amount of adsorption is decreased a little. The small guest enters and leaves the cavity rapidly, whereas larger guests enter slowly due to their size relative to the size of the gaps in the capsule. As a result, the uptake and release of MB from CuBTC is faster than that of CV.     

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

This work honors the 75th birthday of Professor Ionel Michael Navon by presenting original results highlighting the computational efficiency of the adjoint sensitivity analysis methodology for function‐valued operator responses by means of an illustrative paradigm dissolver model. The dissolver model analyzed in this work has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model comprises eight active compartments in which the 16 time‐dependent nonlinear differential equations modeling the physical and chemical processes comprise 619 scalar and time‐dependent model parameters, related to the model's equation of state and inflow conditions. The most important response for the dissolver model is the time‐dependent nitric acid in the compartment furthest away from the inlet, where measurements are available at 307 time instances over the transient's duration of 10.5 h. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed efficiently by applying the adjoint sensitivity analysis methodology for operator‐valued responses. The uncertainties in the model parameters are propagated using the above‐mentioned sensitivities to compute the uncertainties in the computed responses. A predictive modeling formalism is subsequently used to combine the computational results with the experimental information measured in the compartment furthest from the inlet and then predict optimal values and uncertainties throughout the dissolver. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayes' theorem with the “likelihood” provided by the multi‐physics computational models. Finally, the posterior distribution is evaluated using the saddle‐point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multi‐physics models, along with corresponding reduced uncertainties. This work shows that even though the experimental data pertains solely to the compartment furthest from the inlet (where the data were measured), the predictive modeling procedure used herein actually improves the predictions and reduces the predicted uncertainties for the entire dissolver, including the compartment furthest from the measurements, because this predictive modeling methodology combines and transmits information simultaneously over the entire phase‐space, comprising all time steps and spatial locations. Copyright © 2016 John Wiley & Sons, Ltd.     

Synthesis of chromene derivatives in the presence of mordenite zeolite/MIL‐101 (Cr) metal–organic framework composite as catalyst

In the present study, the synthesis of mordenite zeolite/MIL‐101(Cr) metal–organic framework (MOF) composite [MOR/MIL‐101(Cr)] using the ship in a bottle method was suggested. The properties of prepared composite and individual MOF and MOR zeolite were characterized by X‐ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), nitrogen adsorption–desorption measurement, and thermogravimetric analysis (TGA). The XRD results indicated diffraction peaks for each compound (MOR and MOF) in composite. The SEM and TEM images showed the formation of plates MOR (with size of 2.5 × 3 μm) along with spherical particles MIL‐101. The Brunauer–Emmett–Teller results showed that the surface area of the composite was smaller than individual MOF and MOR zeolite. Based on TGA plots, the hybrid zeolite/MOF composite was more thermally stable compared with the isolated MIL‐101(Cr). The composite was functionalized by post‐synthetic modification to obtain acid–base bifunctionality (H‐MOR/MIL‐101‐ED) for the synthesis of chromene derivatives. The acidity from framework Al‐O(H)‐Si sites in MOR and basicity from amine groups in MIL‐101 were obtained by post‐synthetic modification.     

An Anthracene-Based Metal-Organic Framework for Selective Photo-Reduction of Carbon Dioxide to Formic Acid Coupled with Water Oxidation

A Zr-based metal-organic framework has been synthesized and employed as a catalyst for photochemical carbon dioxide reduction coupled with water oxidation. The catalyst shows significant carbon dioxide reduction property with concomitant water oxidation. The catalyst has broad visible light as well as UV light absorption property, which is further confirmed from electronic absorption spectroscopy. Formic acid was the only reduced product from carbon dioxide with a turn-over frequency (TOF) of 0.69 h⁻¹ in addition to oxygen, which was produced with a TOF of 0.54 h⁻¹. No external photosensitizer is used and the ligand itself acts as the light harvester. The efficient and selective photochemical carbon dioxide reduction to formic acid with concomitant water oxidation using Zr-based MOF as catalyst is thus demonstrated here.     

Intramolecular orbital engineered hetero bimetallic Ce-Fe MOF with reduced transition energy and enhanced visible light property

A structurally stable, 3d-4f heterometallic coordination polymer has been solvothermally synthesised and evaluated for its accomplished materials properties. The light absorption activity in the visible band was higher for unique Ce-Fe MOF than that of the homometallic Ce-MOF or Fe- MOF. The intimate overlap of two different metal clusters in heterometallic environmental induced the formation of low line conduction orbital, which ultimately lowered the transition energy. The heterometallic acquired an additional sensitisation from a Fe-μ3-oxo cluster that had vibrantly enhanced the light uptake activity. The vacancy created in the 6s, 5d orbital of Ce in Ce-Fe MOF contributed to the photo-excitation of electrons and reduced the recombination time. This distinct intramolecular arrangement assisted the exciton trapping characteristic. Also, the presence of multiple metal cores in the framework aided to confine the increased number of excitons for a redox reaction. The solar photocatalysis study with acetaminophen revealed these improved materialistic features by degrading it 94.6% with a rate constant of 0.0137 min⁻¹. The recycle studies confirmed the robust stability of the synthesised MOF.     

Switching from linear to cyclic δ‐Polyvalerolactone synthesized via zeolitic imidazolate framework as a catalyst: A promising approach

A series of spray dried zeolitic imidazolate frameworks (ZIFs = ZIF‐8, ZIF‐67, and Zn/Co‐ZIF) are used as a catalyst for the bulk ring‐opening polymerization of δ‐valerolactone without any co‐catalyst to generate polyvalerolactone. Interestingly, using the same catalyst under the same reaction conditions could manipulate the structure of the product polymer, and thus its physical properties. Thus, using a dried substrate leads to the formation of the cyclic polymer while a linear polymer was formed on using the commercially available substrate. An activated monomer mechanism has been suggested where the propagating zinc alkoxide undergoes an intramolecular transesterification to release cyclic or linear polyvalerolactone. The ROP of δ‐VL without drying shows that the polymeric zwitterions have little tendency to cyclize in the presence of moisture. At 140 °C, ZIF‐8 shows a superior catalytic activity resulting in the production of cyclic polyvalerolactone having a high molecular weight as compared to ZIF‐67 or Zn/Co‐ZIF due to the presence of highly active sites. The catalyst could be recycled and reused without any significant loss of catalytic activity.